1. Field of the Invention
This invention relates, generally, to methods of predicting and controlling the drilling trajectory, in directional oil and gas wells, and specifically, to methods which provide a three-dimensional analysis of such a drilling trajectory, and the control of such trajectory, characterized by accounting for the anisotropic drilling characteristics of both the formation and the bit.
2. Description of the Prior Art
Many drillers have sometimes observed rather severe deviations. Deviation angles of up to 60.degree. have sometimes been observed in supposedly vertical wells. Such phenomena were semi-qualitatively explained by several concepts, including the "miniature whipstock theory," which attributed them to the effect of different formation drillabilities.
A. Practices in the control of directional drilling
Improvements in our understanding of the deviation tendencies of various BHA's (Bottomhole Assembly) have come slowly. At the present, there is a heavy reliance on trial and error, though one can use any one of the following existing practices for directional control:
1. Prior experience and standard BHA types (building, dropping, or holding); This is the most common approach; PA1 2. Bit side force as a qualitative measure of deviation tendency; PA1 3. Resultant bit force direction as the actual drilling direction; PA1 4. Borehole curvature that induces zero side force as the actual drilling curvature; and PA1 5. Rock-bit interaction modeling to define the drilling direction. Additionally, one can use the following: PA1 6. Bit axis direction as the projected drilling direction. Methods (2-6) require the use of a suitable BHA analysis program.
In method (1), a suitable type of BHA is selected for a depth region to match the planned borehole curvature, e.g., a building BHA for a building section of the borehole. Though simple, such an approach poses two problems. First, though BHA's do generally behave as expected in a straight hole, their drilling tendencies are strongly influenced by the borehole curvature and inclination, and, to a lesser extent, by the WOB (weight on bit). A "building" BHA will become a dropping assembly in a hole that builds at a sufficient curvature, and vice versa. Second, such a practice does not account for the effects of formation, borehole geometry, and operating conditions. As a result, what worked in one well or depth interval may not work in another. The consequence is that frequent correction runs are needed.
Method (2) is an improvement over method (1) in that it provides a semi-quantitative means of predicting the deviation tendency of a BHA.
Methods (3-6) provide a quantitative prediction of the actual drilling direction. They differ in how the actual drilling trajectory is defined by the known parameters, i.e., by how the "rock-bit interaction" is modeled. The degree of success of each such method lies in how well each model accounts for the relevant parameters affecting the drilling direction. Some of these methods are clearly inadequate because important parameters are neglected.
Due to diminishing world oil reserves, future exploration for fossil fuels will gradually shift to more difficult reservoirs, requiring deeper and/or offshore drilling. In either case, rig costs will be much higher than in conventional land drilling of vertical wells. Thus, more and more emphasis will be placed on directional drilling. At the same time, the increased cost of such rigs has also heightened the need to reduce drilling costs (including the tripping time while drilling) and avoid drilling troubles due to unwanted hole deviations.
Drilling deviation is the result of rock removal under the complex action of the bit. Research on the fundamental problems of rock removal and deviation involve three approaches: (1) laboratory studies, (2) stress calculations, and (3) simplified analytical ("rock-bit interaction") modeling. The first two approaches examine the actual, if simplified, rock removal and drilling deviation under given bit loads, which must include a deviation side force. Results of the tests or analyses hopefully will lead to useful (even if empirically fitted) relations that describe the deviation tendencies of bits in any particular situation.
In terms of the first approach, earlier experimental works dealt primarily with the effects of various drilling conditions on the drilling rate of various bits. Early results confirmed, at least qualitatively, the common observation that both the bit and the formation exhibit anisotropic drilling characteristics. The deviation tendency was found to depend on the bit geometry and dip angle. Early lab drilling tests, using a rock cradle that was subjected to a side force, measured the side and axial penetration rates. Using isotropic rocks, there were cnclusions that bits indeed drill anisotropically.
In terms of the second approach, plasticity theory was employed to study the limit (failure) stress state under a single bit tooth, which was idealized as a 2-D wedge or punch. Early works considered the side force generated on the bit tooth, using simplified 2-D (upper bound) analysis in plasticity. Though useful in providing some insights, these static analyses clearly do not simulate actual drilling conditions. The results are also not easily interpreted in terms of quantitative deviation trends. More recently, a large scale computer program was developed to carry out numerical analysis to study the stimulated dynamic response of PDC bits. The modeling and solution processes are extremely cumbersome and require detailed apriori knowledge of the parameters affecting the system. Most of these data are not available at present (and perhaps for a long time to come). This approach is clearly not yet practical.
Relevant parameters that affect the deviation tendency of a given BHA may be grouped into the following: (1) the BHA configuration (with or without stabilizers); (2) the borehole trajectory and geometry; (3) the operating conditions; (4) the bit; and (5) the formation being drilled. Each of these groups further contain many parameters.
Because of the large numbers of parameters involved, a more fundamental understanding can be achieved only by reducing the number of immediate parameters by rational synthesis and grouping of the contributing effects. Use of a BHA analysis program is required. The pioneering work in this respect was by Lubinski and Woods (Lubinski, A. and Woods, H. B.: "Factors Affecting the Angle of Inclination and Doglegging in Rotary Bore Holes," API Drilling & Prod. Pract., 1953, pp. 222-250; and Woods, H. B. and Lubinski, A.: "Use of Stabilizers in Controlling Hole Deviation," API Drill. & Prod. Pract., 1955, pp. 165-182.) The Lubinski model includes two elements: a 2-D BHA analysis program using a semi-analytic method to predict the side (build/drop) force on the bit in slick assemblies, and a formation anisotropy effect model to account for the commonly experienced up-dip tendency in directional drilling. The Lubinski model defines a rock anisotropy index to account for the different drillabilities parallel and perpendicular to the formation bedding plane. This model assumes bits to be isotropic. A comparison between the existing 2-D analysis and the 3-D methods described hereinafter provides an indication of a significant advance in this art.
Some existing models utilize a 2-D analysis, resulting in only a build/drop prediction. As an example, in assessing the formation effect, I have recently shown that, due to the difference in the apparent dip angle (seen in the common vertical plane) and the true dip angle (tilting away from the vertical plane), the predicted drilling direction (in the common vertical plane) will change. This will affect the result of build/drop prediction. It may also mask the bit anisotropy effect. Parallel arguments exist when one examines only the bit effect.
In a 2-D model, where the entire well bore and drill string are assumed to lie in the same vertical plane, the formation dip is seen as the apparent dip and not the true dip. These angles are equal only when the relative strike angle of the dipping plane is 90.degree.. Otherwise, the apparent dip angle is always smaller than the true dip angle. In the extreme case when the relative strike angle is zero, the apparent dip angle is always zero, even when the true dip angle is 90.degree..
In a 2-D analysis, all relevant vectors are assumed to lie on the common vertical plane, which is the base plane. The formation normal vector is E.sub.da ; the bit force is decomposed into the normal and parallel components OB.sub.a and AB.sub.a. Anisotropy of the formation would cause the apparent drilling vector E.sub.ra to pass through the point C.sub.a. The ratio C.sub.a B.sub.a /AB.sub.a describes the degree of anisotropy of the formation, which is an anisotropy index. Vector E.sub.ra also lies in the same base plane. Thus, no walk is predicted.
In a 3-D analysis, one uses the true formation normal vector E.sub.d, which in this particular case points above the base plane. The similar bit force components are OB and AB, and the drilling direction E.sub.r passes through the point C. The ratio CB/AB is again the anisotropy index, which is also the same as C.sub.p B.sub.p /AB.sub.p (where the subscript p denotes the projection onto the base plane) due to parallel projections. We can then conclude that the line C.sub.a C.sub.p is parallel to the vector E.sub.da, and therefore cannot be parallel to the vector E.sub.ra. In other words, the vector E.sub.r does not project into the vector E.sub.ra. Additionally, the 3-D analysis also results in a walk component of E.sub.r pointing above the base plane.
Using 3-D vector analysis, one can derive the in-plane build-drop deviation angle A.sub.a (from 2-D analysis) and A.sub.p (from projected 3-D analysis), relative to the bit force vector, as follows: ##EQU1## Here A.sub.fda is the angle between the bit force and the 2-D formation normal, and A.sub.dn is the angle between the 3-D and 2-D formation normal vectors. A.sub.a is always greater than A.sub.p, A.sub.a and A.sub.p being the angles between E.sub.f and E.sub.ra, and E.sub.f and E.sub.rp, respectively.
It is conceivable that the true drilling direction might have a building tendency while the apparent drilling direction might show a dropping tendency, or vice versa. In anisotropic formations, there are only two exceptions to the above conclusion: when the relative strike angle A.sub.r is 90.degree. or 0.degree..
1. If A.sub.r is 90.degree.: Then the 2-D and 3-D analyses in fact coincide. A subsidiary case of this is when the true dip angle is zero. Then, the strike direction of the bedding normal is arbitrary, and can be set to 90.degree..
2. If A.sub.r is zero: Then formation anisotropy causes only walk deviation but no build/drop deviation.
Nevertheless, since its inception in 1953, the Lubinski model has stood for a long time as the only rationally derived rock-bit interaction model.
Recently, Brett et al developed a bit effect model. (Brett, J. F.; Gray, J. A.; Bell, R. K. and Dunbar, M. E.: "A Method of Modeling the Directional Behavior of Bottomhole Assemblies Including Those with Bent Subs and Downhole Motors," SPE/IADC conference, February 1986, Dallas. SPE Paper 14767.) Their model accounts for the anisotropic effects of the bit, but assumed the formation to be isotropic. Others have developed a bit effect model that is coupled with BHA analysis, though their model in effect assumes the drilling direction to be coincident with the bit force.
It is therefore the primary object of the present invention to provide new and improved methods for predicting the drilling trajectory in a directional well.
It is another object of the present invention, used in the inverse mode, to provide new and improved methods for determining the anisotropic rock and bit indices involved in drilling an earth borehole through an earth formation.
It is still another object of the present invention to provide new and improved methods for producing drilling dip logs.
It is yet another object of the invention to provide new and improved drilling bit wear logs and drilling lithology index logs.
It is still another object of the invention to provide methods of controlling the drilling trajectory in directional wells.